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[[Image:999 Perspective.png|left|130px|A view of 0.999... in rectangular perspective]]
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'''[[0.999...]]''' (also denoted <math>0.\bar{9}</math> or <math>0.\dot{9}</math>) is a [[recurring decimal]] which is [[equality (mathematics)|exactly equal]] to [[1 (number)|1]]. In other words, the symbols 0.999… and 1 represent the same real number. Mathematicians have formulated a number of [[mathematical proof|proof]]s of this identity, which vary with their level of [[rigor]], preferred development of the real numbers, background assumptions, historical context and target audience. The equality 0.999… = 1 has long been taught in textbooks, and in the last few decades, researchers of [[mathematics education]] have studied the reception of this equation among students, who often vocally reject the equality. Their reasoning is often based on an expectation that [[infinitesimal]] quantities should exist, that [[arithmetic]] may be broken, or simply that 0.999… should have a last 9. These ideas are false in the [[real number]]s, as can be proven by explicitly constructing the reals from the [[rational number]]s, and such constructions can also prove that 0.999… = 1 directly. ('''[[0.999...|more...]]''')

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